MHB Two Balls Thrown Vertical Upward

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The discussion focuses on the physics of two balls thrown vertically upward from different heights and with different initial speeds. The height of each ball over time is modeled by the equation h(t) = -16t² + v₀t + h₀, where h₀ is the initial height and v₀ is the initial velocity. To determine which ball hits the ground first, the formula must be applied separately for each ball, solving for the time t when h(t) equals zero. The ball with the smaller t value will hit the ground first, regardless of its speed upon impact. The conversation also touches on the quadratic formula's application in similar scenarios, including objects thrown downward.
  • #31
Ok. Great. Let us move on. I will post similar word problems in the coming days.
 
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  • #32
Okay, so we've found:

$$t=\frac{v_0\pm\sqrt{v_0^2-2a\Delta x}}{a}$$

Suppose we have $\Delta x=0$. At what times does that occur?
 
  • #33
MarkFL said:
Okay, so we've found:

$$t=\frac{v_0\pm\sqrt{v_0^2-2a\Delta x}}{a}$$

Suppose we have $\Delta x=0$. At what times does that occur?

Replace (delta)x with 0 and simplify, right?
 
  • #34
RTCNTC said:
Replace (delta)x with 0 and simplify, right?

Yes. :)
 
  • #35
Thank you for all your help.
 
  • #36
Um, okay.

I was attempting to share with you some of the ways I used to go about learning things that helped me succeed in my math studies, but if you just wish to walk away from that, then so be it. Examining formulas at the boundaries of the parameter values gave me a good number of "aha" moments. Looking at how one values changes in relation to another is also illuminating.

images
 
  • #37
MarkFL said:
Um, okay.

I was attempting to share with you some of the ways I used to go about learning things that helped me succeed in my math studies, but if you just wish to walk away from that, then so be it. Examining formulas at the boundaries of the parameter values gave me a good number of "aha" moments. Looking at how one values changes in relation to another is also illuminating.

I thank you for helping me as I march on my way to succeed with word problems.
 

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